Stan code for the analysis of my Social and Cultural Dynamics exam

Plate notation

stan code

## //modell
## data{
##     // number of data points, groups, and vowels
##     int<lower=1> N;
##     int<lower=1> N_group;
##     int<lower=1> N_vowel;
##     
##     // binomial data for the two psychometric functions
##     int k_ind[N];
##     int k_gro[N];
##     int n_ind[N];
##     int n_gro[N];
##     
##     // input data
##     int group[N];
##     int intensity[N];
##     int vowel[N];
##     
##     
##     // collective benefit model
##     real local_confidence[N_group];
##     
## }
## 
## 
## parameters{
##     
##     // less important note: I tried two different parametrisations of the random slope-intercept covariance,
##     // and couldn't get the cholesky decomposition to work 
##     // ==================================
##     // Option 1) specify var-covar matrices manually
##     vector[2] gv_group[N_group];
##     vector[2] gv_vowel[N_vowel];
##     vector[2] iv_group[N_group];
##     vector[2] iv_vowel[N_vowel];
##     
##     corr_matrix[2] gRho_group;
##     corr_matrix[2] gRho_vowel;
##     corr_matrix[2] iRho_group;
##     corr_matrix[2] iRho_vowel;
##     
##     
##     
##     // =========================================
##     // Option 2: cholesky decomposition
##     // cholesky_factor_corr[2] gL_group;
##     // vector<lower=0>[2] gcsigma_group;
##     // cholesky_factor_corr[2] gL_vowel;
##     // vector<lower=0>[2] gcsigma_vowel;
##     // 
##     // cholesky_factor_corr[2] iL_group;
##     // vector<lower=0>[2] icsigma_group;
##     // cholesky_factor_corr[2] iL_vowel;
##     // vector<lower=0>[2] icsigma_vowel;
## 
##     
##     // scale parameters for the random effects
##     vector<lower=0>[2] gsigma_group;
##     vector<lower=0>[2] gsigma_vowel;
##     vector<lower=0>[2] isigma_group;
##     vector<lower=0>[2] isigma_vowel;
##     
##     // main effects
##     real ga;
##     real gb;
##     real ia;
##     real ib;
##     
##     
##     // =========================================================
##     // parameters for the collective benefit model
##     // real collective_mu;
##     real<lower=0> collective_sigma;
##     // 
##     real col_a;
##     real col_b_confidence;
##     
## 
## }
## transformed parameters{
##     real<lower=0> collective_benefit[N_group];
##     for ( k in 1:N_group ) {
##         collective_benefit[k] = inv_logit(
##             gv_group[k,2] * gsigma_group[2])
##         / inv_logit(
##             iv_group[k,2] * isigma_group[2]);
##         // collective_benefit[i] = inv_logit(gb) - inv_logit(ib);
##     }
##     
## }
## 
## 
## model{
##     
##     // logit(theta) = A + B * data
##     vector[N] gtheta;
##     vector[N] gA;
##     vector[N] gB;
##     
##     vector[N] itheta;
##     vector[N] iA;
##     vector[N] iB;
##     
##     real collective_mu[N];
##     
##     ia ~ normal(0, 1);
##     ib ~ normal(0, 1);
##     ga ~ normal(0, 1);
##     gb ~ normal(0, 1);
##     
##     
##     // scale of the random effects
##     gsigma_group ~ cauchy( 0 , 2 );
##     gsigma_vowel ~ cauchy( 0 , 2 );
##     isigma_group ~ cauchy( 0 , 2 );
##     isigma_vowel ~ cauchy( 0 , 2 );
##     
##     
##     
##     // ==================================
##     // 1) specify var-covar matrices manually
##     // correlations of the random effects
##     gv_group ~ multi_normal(rep_vector(0,2), gRho_group);
##     gv_vowel ~ multi_normal(rep_vector(0,2), gRho_vowel);
##     iv_group ~ multi_normal(rep_vector(0,2), iRho_group);
##     iv_vowel ~ multi_normal(rep_vector(0,2), iRho_vowel);
##     
##     
##     gRho_group ~ lkj_corr( 4 );
##     gRho_vowel ~ lkj_corr( 4 );
##     iRho_group ~ lkj_corr( 4 );
##     iRho_vowel ~ lkj_corr( 4 );
##     
##     
##     
##     // =========================================
##     // 2: cholesky decomposition
##     // cholesky stuff - gives me high Rhat and constant L=1
##     // gv_group ~ multi_normal_cholesky( rep_vector(0,2) ,  diag_pre_multiply(gcsigma_group, gL_group));
##     // gv_vowel ~ multi_normal_cholesky( rep_vector(0,2) ,  diag_pre_multiply(gcsigma_vowel, gL_vowel));
##     // gcsigma_vowel ~ cauchy(0,2);
##     // gcsigma_group ~ cauchy(0,2);
##     // gL_group ~ lkj_corr_cholesky(4);
##     // gL_vowel ~ lkj_corr_cholesky(4);
##     // 
##     // iv_group ~ multi_normal_cholesky( rep_vector(0,2) ,  diag_pre_multiply(icsigma_group, iL_group));
##     // iv_vowel ~ multi_normal_cholesky( rep_vector(0,2) ,  diag_pre_multiply(icsigma_vowel, iL_vowel));
##     // icsigma_vowel ~ cauchy(0,2);
##     // icsigma_group ~ cauchy(0,2);
##     // iL_group ~ lkj_corr_cholesky(4);
##     // iL_vowel ~ lkj_corr_cholesky(4);
## 
##     
##     
##     
##     
##     // psychometric function for both individuals and groups
##     for ( i in 1:N ) {
##         gA[i] = ga + gv_vowel[vowel[i],1] * gsigma_vowel[1] + gv_group[group[i],1] * gsigma_group[1]; 
##         gB[i] = gb + gv_vowel[vowel[i],2] * gsigma_vowel[2] + gv_group[group[i],2] * gsigma_group[2];
##         gtheta[i] =  gA[i] + gB[i] * intensity[i];
##         
##         iA[i] = ia + iv_vowel[vowel[i],1] * isigma_vowel[1] + iv_group[group[i],1] * isigma_group[1]; 
##         iB[i] = gb + iv_vowel[vowel[i],2] * isigma_vowel[2] + iv_group[group[i],2] * isigma_group[2];
##         itheta[i] =  iA[i] + iB[i] * intensity[i];
##     }
##     k_gro ~ binomial_logit(n_gro, gtheta);
##     k_ind ~ binomial_logit(n_ind, itheta);
##     
##     
##     
##     // here comes the collective benefit stuff
##     // not sure if I should do something something with a jacobian b/c of sampling a transformed parameter
##     
##     for ( k in 1:N_group ) {
##     //     collective_mu[k] = col_a + col_b_confidence * local_confidence[k];
##         collective_benefit[k] ~ normal(col_a, 1 );
##     }
##     
##     col_a ~ normal(1,1);
##     // col_b_confidence ~ normal(0,1);
##     // collective_sigma ~ cauchy(0,2);
##     
##     // collective_benefit[k] ~ normal(1, 1);
##     // collective_benefit[k] ~ gamma(3, 2);
##     
##     
##     
## // generated quantities{
## }
## //     // =========================================
## //     // 2: cholesky decomposition
## //     // transform cholesky stuff back to var-covar matrixes
## //     matrix[2,2] gO_group;
## //     matrix[2,2] gSigma_group;
## //     matrix[2,2] gO_vowel;
## //     matrix[2,2] gSigma_vowel;
## //     matrix[2,2] iO_group;
## //     matrix[2,2] iSigma_group;
## //     matrix[2,2] iO_vowel;
## //     matrix[2,2] iSigma_vowel;
## //     
## //     gO_group = multiply_lower_tri_self_transpose(gL_group);
## //     gSigma_group = quad_form_diag(gO_group, gcsigma_group); 
## //     gO_vowel = multiply_lower_tri_self_transpose(gL_vowel);
## //     gSigma_vowel = quad_form_diag(gO_vowel, gcsigma_vowel); 
## //     
## //     iO_group = multiply_lower_tri_self_transpose(iL_group);
## //     iSigma_group = quad_form_diag(iO_group, icsigma_group); 
## //     iO_vowel = multiply_lower_tri_self_transpose(iL_vowel);
## //     iSigma_vowel = quad_form_diag(iO_vowel, icsigma_vowel); 
## // }

## Inference for Stan model: model.
## 4 chains, each with iter=10000; warmup=5000; thin=1; 
## post-warmup draws per chain=5000, total post-warmup draws=20000.
## 
##                                 mean  se_mean       sd           2.5%
## gv_group[1,1]          -5.800000e-01     0.02     0.81  -2.150000e+00
## gv_group[1,2]          -1.800000e-01     0.02     0.46  -1.100000e+00
## gv_group[2,1]           7.600000e-01     0.03     0.82  -9.900000e-01
## gv_group[2,2]          -8.100000e-01     0.02     0.48  -1.830000e+00
## gv_group[3,1]          -1.190000e+00     0.03     0.88  -2.810000e+00
## gv_group[3,2]           5.100000e-01     0.02     0.56  -5.000000e-01
## gv_group[4,1]          -2.400000e-01     0.02     0.76  -1.700000e+00
## gv_group[4,2]           5.800000e-01     0.02     0.48  -2.800000e-01
## gv_group[5,1]           3.000000e-02     0.02     0.76  -1.450000e+00
## gv_group[5,2]           8.700000e-01     0.02     0.51  -7.000000e-02
## gv_group[6,1]           2.300000e-01     0.02     0.84  -1.550000e+00
## gv_group[6,2]          -1.080000e+00     0.02     0.52  -2.150000e+00
## gv_group[7,1]           1.700000e-01     0.02     0.77  -1.370000e+00
## gv_group[7,2]          -3.700000e-01     0.02     0.44  -1.270000e+00
## gv_group[8,1]          -8.000000e-02     0.02     0.80  -1.650000e+00
## gv_group[8,2]           1.390000e+00     0.02     0.57   3.500000e-01
## gv_group[9,1]           2.500000e-01     0.02     0.86  -1.510000e+00
## gv_group[9,2]          -7.300000e-01     0.02     0.49  -1.770000e+00
## gv_vowel[1,1]           2.400000e-01     0.03     0.58  -7.100000e-01
## gv_vowel[1,2]           8.000000e-02     0.02     0.43  -7.800000e-01
## gv_vowel[2,1]          -1.100000e+00     0.02     0.52  -2.250000e+00
## gv_vowel[2,2]           9.900000e-01     0.02     0.59   6.000000e-02
## gv_vowel[3,1]           2.800000e-01     0.02     0.58  -6.900000e-01
## gv_vowel[3,2]          -1.030000e+00     0.02     0.56  -2.310000e+00
## gv_vowel[4,1]          -1.110000e+00     0.01     0.50  -2.210000e+00
## gv_vowel[4,2]           3.000000e-01     0.02     0.45  -5.000000e-01
## iv_group[1,1]          -1.200000e-01     0.03     0.86  -1.780000e+00
## iv_group[1,2]          -8.200000e-01     0.02     0.56  -1.920000e+00
## iv_group[2,1]           3.400000e-01     0.03     0.93  -1.500000e+00
## iv_group[2,2]          -1.180000e+00     0.02     0.62  -2.460000e+00
## iv_group[3,1]          -2.600000e-01     0.02     0.80  -1.790000e+00
## iv_group[3,2]           1.000000e-01     0.02     0.62  -1.150000e+00
## iv_group[4,1]          -5.800000e-01     0.03     0.89  -2.360000e+00
## iv_group[4,2]           9.600000e-01     0.02     0.68  -3.100000e-01
## iv_group[5,1]           3.500000e-01     0.02     0.80  -1.320000e+00
## iv_group[5,2]           6.400000e-01     0.02     0.62  -5.600000e-01
## iv_group[6,1]          -3.200000e-01     0.02     0.85  -2.000000e+00
## iv_group[6,2]          -1.200000e-01     0.02     0.66  -1.410000e+00
## iv_group[7,1]          -1.600000e-01     0.02     0.81  -1.690000e+00
## iv_group[7,2]          -3.000000e-01     0.02     0.58  -1.400000e+00
## iv_group[8,1]           6.700000e-01     0.02     0.85  -1.110000e+00
## iv_group[8,2]           9.200000e-01     0.02     0.72  -4.700000e-01
## iv_group[9,1]          -4.800000e-01     0.03     0.88  -2.190000e+00
## iv_group[9,2]          -1.600000e-01     0.02     0.65  -1.420000e+00
## iv_vowel[1,1]           4.000000e-01     0.02     0.75  -9.300000e-01
## iv_vowel[1,2]           2.900000e-01     0.03     0.75  -1.210000e+00
## iv_vowel[2,1]          -6.300000e-01     0.02     0.76  -2.100000e+00
## iv_vowel[2,2]           6.600000e-01     0.02     0.71  -6.500000e-01
## iv_vowel[3,1]          -9.000000e-02     0.02     0.74  -1.470000e+00
## iv_vowel[3,2]          -3.800000e-01     0.02     0.67  -1.730000e+00
## iv_vowel[4,1]          -5.300000e-01     0.02     0.77  -2.010000e+00
## iv_vowel[4,2]          -5.500000e-01     0.02     0.71  -2.040000e+00
## gRho_group[1,1]         1.000000e+00     0.00     0.00   1.000000e+00
## gRho_group[1,2]        -2.300000e-01     0.01     0.32  -7.600000e-01
## gRho_group[2,1]        -2.300000e-01     0.01     0.32  -7.600000e-01
## gRho_group[2,2]         1.000000e+00     0.00     0.00   1.000000e+00
## gRho_vowel[1,1]         1.000000e+00     0.00     0.00   1.000000e+00
## gRho_vowel[1,2]        -1.800000e-01     0.01     0.31  -7.300000e-01
## gRho_vowel[2,1]        -1.800000e-01     0.01     0.31  -7.300000e-01
## gRho_vowel[2,2]         1.000000e+00     0.00     0.00   1.000000e+00
## iRho_group[1,1]         1.000000e+00     0.00     0.00   1.000000e+00
## iRho_group[1,2]        -1.300000e-01     0.01     0.34  -7.300000e-01
## iRho_group[2,1]        -1.300000e-01     0.01     0.34  -7.300000e-01
## iRho_group[2,2]         1.000000e+00     0.00     0.00   1.000000e+00
## iRho_vowel[1,1]         1.000000e+00     0.00     0.00   1.000000e+00
## iRho_vowel[1,2]        -5.000000e-02     0.01     0.33  -6.500000e-01
## iRho_vowel[2,1]        -5.000000e-02     0.01     0.33  -6.500000e-01
## iRho_vowel[2,2]         1.000000e+00     0.00     0.00   1.000000e+00
## gsigma_group[1]         4.900000e-01     0.01     0.31   3.000000e-02
## gsigma_group[2]         8.000000e-02     0.00     0.03   4.000000e-02
## gsigma_vowel[1]         1.620000e+00     0.04     0.91   5.800000e-01
## gsigma_vowel[2]         1.100000e-01     0.00     0.06   4.000000e-02
## isigma_group[1]         4.600000e-01     0.01     0.32   3.000000e-02
## isigma_group[2]         6.000000e-02     0.00     0.02   2.000000e-02
## isigma_vowel[1]         6.600000e-01     0.02     0.59   5.000000e-02
## isigma_vowel[2]         6.000000e-02     0.00     0.05   1.000000e-02
## ga                     -1.250000e+00     0.03     0.74  -2.450000e+00
## gb                      1.800000e-01     0.00     0.03   1.200000e-01
## ia                     -1.550000e+00     0.02     0.48  -2.320000e+00
## ib                     -4.000000e-02     0.03     1.01  -2.030000e+00
## collective_sigma       9.179058e+307      Inf      Inf  5.119840e+306
## col_a                   1.000000e+00     0.01     0.32   3.800000e-01
## col_b_confidence       -1.281625e+04 10352.36 19806.72  -5.791971e+04
## collective_benefit[1]   1.020000e+00     0.00     0.02   9.700000e-01
## collective_benefit[2]   1.000000e+00     0.00     0.03   9.500000e-01
## collective_benefit[3]   1.020000e+00     0.00     0.03   9.700000e-01
## collective_benefit[4]   9.900000e-01     0.00     0.03   9.400000e-01
## collective_benefit[5]   1.020000e+00     0.00     0.02   9.700000e-01
## collective_benefit[6]   9.600000e-01     0.00     0.03   9.100000e-01
## collective_benefit[7]   9.900000e-01     0.00     0.02   9.500000e-01
## collective_benefit[8]   1.030000e+00     0.00     0.03   9.800000e-01
## collective_benefit[9]   9.800000e-01     0.00     0.02   9.200000e-01
## lp__                   -3.909000e+02     0.30     8.41  -4.077200e+02
##                                  25%            50%           75%
## gv_group[1,1]          -1.100000e+00  -6.000000e-01  -7.00000e-02
## gv_group[1,2]          -4.900000e-01  -1.900000e-01   1.10000e-01
## gv_group[2,1]           2.500000e-01   7.800000e-01   1.31000e+00
## gv_group[2,2]          -1.120000e+00  -7.900000e-01  -4.90000e-01
## gv_group[3,1]          -1.780000e+00  -1.230000e+00  -6.70000e-01
## gv_group[3,2]           1.200000e-01   4.700000e-01   8.70000e-01
## gv_group[4,1]          -7.400000e-01  -2.700000e-01   2.30000e-01
## gv_group[4,2]           2.500000e-01   5.500000e-01   8.70000e-01
## gv_group[5,1]          -4.500000e-01   1.000000e-02   5.10000e-01
## gv_group[5,2]           5.300000e-01   8.400000e-01   1.20000e+00
## gv_group[6,1]          -3.100000e-01   2.400000e-01   7.90000e-01
## gv_group[6,2]          -1.410000e+00  -1.050000e+00  -7.20000e-01
## gv_group[7,1]          -3.300000e-01   1.800000e-01   6.80000e-01
## gv_group[7,2]          -6.500000e-01  -3.600000e-01  -7.00000e-02
## gv_group[8,1]          -5.700000e-01  -1.100000e-01   4.10000e-01
## gv_group[8,2]           9.900000e-01   1.360000e+00   1.75000e+00
## gv_group[9,1]          -3.100000e-01   2.600000e-01   8.10000e-01
## gv_group[9,2]          -1.030000e+00  -7.100000e-01  -4.00000e-01
## gv_vowel[1,1]          -1.700000e-01   1.600000e-01   6.00000e-01
## gv_vowel[1,2]          -1.900000e-01   6.000000e-02   3.30000e-01
## gv_vowel[2,1]          -1.400000e+00  -1.060000e+00  -7.40000e-01
## gv_vowel[2,2]           5.600000e-01   9.200000e-01   1.34000e+00
## gv_vowel[3,1]          -1.400000e-01   2.100000e-01   6.30000e-01
## gv_vowel[3,2]          -1.370000e+00  -9.700000e-01  -6.20000e-01
## gv_vowel[4,1]          -1.410000e+00  -1.070000e+00  -7.50000e-01
## gv_vowel[4,2]           1.000000e-02   2.700000e-01   5.60000e-01
## iv_group[1,1]          -6.800000e-01  -1.300000e-01   4.50000e-01
## iv_group[1,2]          -1.180000e+00  -8.100000e-01  -4.50000e-01
## iv_group[2,1]          -2.800000e-01   3.600000e-01   9.80000e-01
## iv_group[2,2]          -1.580000e+00  -1.150000e+00  -7.60000e-01
## iv_group[3,1]          -7.900000e-01  -2.800000e-01   2.80000e-01
## iv_group[3,2]          -3.000000e-01   1.000000e-01   4.90000e-01
## iv_group[4,1]          -1.160000e+00  -5.900000e-01  -3.00000e-02
## iv_group[4,2]           5.100000e-01   9.200000e-01   1.39000e+00
## iv_group[5,1]          -1.500000e-01   3.800000e-01   8.80000e-01
## iv_group[5,2]           2.400000e-01   6.300000e-01   1.04000e+00
## iv_group[6,1]          -8.800000e-01  -3.200000e-01   2.30000e-01
## iv_group[6,2]          -5.400000e-01  -1.500000e-01   2.90000e-01
## iv_group[7,1]          -7.000000e-01  -1.800000e-01   3.50000e-01
## iv_group[7,2]          -6.700000e-01  -3.000000e-01   6.00000e-02
## iv_group[8,1]           1.500000e-01   6.900000e-01   1.22000e+00
## iv_group[8,2]           4.500000e-01   9.200000e-01   1.39000e+00
## iv_group[9,1]          -1.050000e+00  -4.900000e-01   1.00000e-01
## iv_group[9,2]          -5.800000e-01  -1.800000e-01   2.40000e-01
## iv_vowel[1,1]          -1.300000e-01   3.500000e-01   8.70000e-01
## iv_vowel[1,2]          -1.700000e-01   2.600000e-01   7.50000e-01
## iv_vowel[2,1]          -1.110000e+00  -6.400000e-01  -1.60000e-01
## iv_vowel[2,2]           1.900000e-01   6.000000e-01   1.10000e+00
## iv_vowel[3,1]          -5.700000e-01  -1.300000e-01   3.60000e-01
## iv_vowel[3,2]          -7.900000e-01  -3.700000e-01   4.00000e-02
## iv_vowel[4,1]          -1.020000e+00  -5.400000e-01  -7.00000e-02
## iv_vowel[4,2]          -9.900000e-01  -5.300000e-01  -1.10000e-01
## gRho_group[1,1]         1.000000e+00   1.000000e+00   1.00000e+00
## gRho_group[1,2]        -4.600000e-01  -2.600000e-01  -1.00000e-02
## gRho_group[2,1]        -4.600000e-01  -2.600000e-01  -1.00000e-02
## gRho_group[2,2]         1.000000e+00   1.000000e+00   1.00000e+00
## gRho_vowel[1,1]         1.000000e+00   1.000000e+00   1.00000e+00
## gRho_vowel[1,2]        -4.000000e-01  -2.000000e-01   3.00000e-02
## gRho_vowel[2,1]        -4.000000e-01  -2.000000e-01   3.00000e-02
## gRho_vowel[2,2]         1.000000e+00   1.000000e+00   1.00000e+00
## iRho_group[1,1]         1.000000e+00   1.000000e+00   1.00000e+00
## iRho_group[1,2]        -3.900000e-01  -1.500000e-01   1.10000e-01
## iRho_group[2,1]        -3.900000e-01  -1.500000e-01   1.10000e-01
## iRho_group[2,2]         1.000000e+00   1.000000e+00   1.00000e+00
## iRho_vowel[1,1]         1.000000e+00   1.000000e+00   1.00000e+00
## iRho_vowel[1,2]        -2.900000e-01  -6.000000e-02   1.80000e-01
## iRho_vowel[2,1]        -2.900000e-01  -6.000000e-02   1.80000e-01
## iRho_vowel[2,2]         1.000000e+00   1.000000e+00   1.00000e+00
## gsigma_group[1]         2.500000e-01   4.500000e-01   6.60000e-01
## gsigma_group[2]         6.000000e-02   7.000000e-02   9.00000e-02
## gsigma_vowel[1]         1.000000e+00   1.380000e+00   1.99000e+00
## gsigma_vowel[2]         7.000000e-02   9.000000e-02   1.30000e-01
## isigma_group[1]         2.100000e-01   4.000000e-01   6.30000e-01
## isigma_group[2]         4.000000e-02   5.000000e-02   7.00000e-02
## isigma_vowel[1]         2.800000e-01   5.100000e-01   8.50000e-01
## isigma_vowel[2]         3.000000e-02   5.000000e-02   7.00000e-02
## ga                     -1.770000e+00  -1.340000e+00  -8.10000e-01
## gb                      1.600000e-01   1.800000e-01   2.00000e-01
## ia                     -1.860000e+00  -1.610000e+00  -1.32000e+00
## ib                     -7.100000e-01  -4.000000e-02   6.50000e-01
## collective_sigma       4.688335e+307  9.308606e+307  1.36593e+308
## col_a                   7.700000e-01   9.900000e-01   1.21000e+00
## col_b_confidence       -2.938946e+04  -2.245370e+03   2.02157e+03
## collective_benefit[1]   1.000000e+00   1.020000e+00   1.03000e+00
## collective_benefit[2]   9.800000e-01   1.000000e+00   1.02000e+00
## collective_benefit[3]   1.000000e+00   1.020000e+00   1.03000e+00
## collective_benefit[4]   9.800000e-01   1.000000e+00   1.01000e+00
## collective_benefit[5]   1.000000e+00   1.020000e+00   1.03000e+00
## collective_benefit[6]   9.500000e-01   9.600000e-01   9.80000e-01
## collective_benefit[7]   9.800000e-01   9.900000e-01   1.01000e+00
## collective_benefit[8]   1.010000e+00   1.030000e+00   1.04000e+00
## collective_benefit[9]   9.600000e-01   9.800000e-01   9.90000e-01
## lp__                   -3.964900e+02  -3.908100e+02  -3.85170e+02
##                                97.5% n_eff Rhat
## gv_group[1,1]           1.130000e+00  1171 1.00
## gv_group[1,2]           7.400000e-01   679 1.01
## gv_group[2,1]           2.320000e+00   725 1.01
## gv_group[2,2]           7.000000e-02   875 1.01
## gv_group[3,1]           7.000000e-01   915 1.00
## gv_group[3,2]           1.690000e+00   715 1.00
## gv_group[4,1]           1.360000e+00  1152 1.00
## gv_group[4,2]           1.610000e+00   776 1.01
## gv_group[5,1]           1.610000e+00  1167 1.00
## gv_group[5,2]           1.920000e+00   759 1.01
## gv_group[6,1]           1.860000e+00  1215 1.00
## gv_group[6,2]          -1.400000e-01   952 1.00
## gv_group[7,1]           1.710000e+00  1379 1.01
## gv_group[7,2]           4.600000e-01   825 1.01
## gv_group[8,1]           1.560000e+00  1202 1.00
## gv_group[8,2]           2.570000e+00   770 1.01
## gv_group[9,1]           1.930000e+00  1249 1.00
## gv_group[9,2]           2.100000e-01   973 1.00
## gv_vowel[1,1]           1.550000e+00   544 1.01
## gv_vowel[1,2]           1.000000e+00   816 1.01
## gv_vowel[2,1]          -1.900000e-01   971 1.01
## gv_vowel[2,2]           2.320000e+00   747 1.00
## gv_vowel[3,1]           1.560000e+00   568 1.01
## gv_vowel[3,2]          -1.500000e-01   641 1.00
## gv_vowel[4,1]          -2.400000e-01  1174 1.00
## gv_vowel[4,2]           1.300000e+00   817 1.01
## iv_group[1,1]           1.600000e+00  1171 1.00
## iv_group[1,2]           2.600000e-01  1116 1.00
## iv_group[2,1]           2.120000e+00   903 1.00
## iv_group[2,2]          -2.000000e-02  1050 1.01
## iv_group[3,1]           1.350000e+00  1292 1.01
## iv_group[3,2]           1.330000e+00  1102 1.00
## iv_group[4,1]           1.250000e+00   978 1.00
## iv_group[4,2]           2.380000e+00   961 1.00
## iv_group[5,1]           1.860000e+00  1134 1.00
## iv_group[5,2]           1.890000e+00  1012 1.00
## iv_group[6,1]           1.380000e+00  1251 1.00
## iv_group[6,2]           1.260000e+00  1149 1.01
## iv_group[7,1]           1.460000e+00  1379 1.00
## iv_group[7,2]           8.900000e-01   992 1.00
## iv_group[8,1]           2.280000e+00  1222 1.00
## iv_group[8,2]           2.330000e+00   878 1.00
## iv_group[9,1]           1.270000e+00  1223 1.00
## iv_group[9,2]           1.200000e+00   994 1.00
## iv_vowel[1,1]           2.020000e+00  1099 1.00
## iv_vowel[1,2]           1.900000e+00   844 1.01
## iv_vowel[2,1]           9.500000e-01  1004 1.00
## iv_vowel[2,2]           2.180000e+00   970 1.00
## iv_vowel[3,1]           1.530000e+00  1032 1.00
## iv_vowel[3,2]           9.100000e-01  1024 1.00
## iv_vowel[4,1]           1.120000e+00  1091 1.00
## iv_vowel[4,2]           8.600000e-01   915 1.00
## gRho_group[1,1]         1.000000e+00 20000  NaN
## gRho_group[1,2]         4.500000e-01   706 1.00
## gRho_group[2,1]         4.500000e-01   706 1.00
## gRho_group[2,2]         1.000000e+00 18793 1.00
## gRho_vowel[1,1]         1.000000e+00 20000  NaN
## gRho_vowel[1,2]         4.700000e-01  1239 1.00
## gRho_vowel[2,1]         4.700000e-01  1239 1.00
## gRho_vowel[2,2]         1.000000e+00 18935 1.00
## iRho_group[1,1]         1.000000e+00 20000  NaN
## iRho_group[1,2]         5.400000e-01   860 1.00
## iRho_group[2,1]         5.400000e-01   860 1.00
## iRho_group[2,2]         1.000000e+00 18931 1.00
## iRho_vowel[1,1]         1.000000e+00 20000  NaN
## iRho_vowel[1,2]         6.100000e-01  1278 1.00
## iRho_vowel[2,1]         6.100000e-01  1278 1.00
## iRho_vowel[2,2]         1.000000e+00 18977 1.00
## gsigma_group[1]         1.200000e+00   769 1.00
## gsigma_group[2]         1.500000e-01   773 1.00
## gsigma_vowel[1]         4.000000e+00   582 1.01
## gsigma_vowel[2]         2.900000e-01   931 1.00
## isigma_group[1]         1.230000e+00   708 1.01
## isigma_group[2]         1.200000e-01   730 1.00
## isigma_vowel[1]         2.250000e+00   727 1.01
## isigma_vowel[2]         1.900000e-01  1015 1.00
## ga                      4.800000e-01   499 1.01
## gb                      2.500000e-01   667 1.00
## ia                     -4.300000e-01   576 1.01
## ib                      1.950000e+00  1632 1.00
## collective_sigma       1.752902e+308 20000  NaN
## col_a                   1.630000e+00  1581 1.00
## col_b_confidence        8.234410e+03     4 2.97
## collective_benefit[1]   1.060000e+00   981 1.01
## collective_benefit[2]   1.060000e+00   829 1.01
## collective_benefit[3]   1.080000e+00   836 1.00
## collective_benefit[4]   1.040000e+00   735 1.01
## collective_benefit[5]   1.060000e+00   986 1.00
## collective_benefit[6]   1.010000e+00   995 1.00
## collective_benefit[7]   1.040000e+00   919 1.01
## collective_benefit[8]   1.080000e+00  1039 1.01
## collective_benefit[9]   1.020000e+00  1025 1.00
## lp__                   -3.749000e+02   784 1.00
## 
## Samples were drawn using NUTS(diag_e) at Mon May 22 14:26:35 2017.
## For each parameter, n_eff is a crude measure of effective sample size,
## and Rhat is the potential scale reduction factor on split chains (at 
## convergence, Rhat=1).